This paper describes some exotic scattering properties of a one-dimensional network of thermoacoustic cells and characterizes them experimentally. The considered two-port consists of a waveguide containing a periodic arrangement of porous materials subjected to temperature gradients and separated by empty sections. The interaction of an acoustic wave with the temperature gradients leads to an inherently nonreciprocal phenomenon known as the thermoacoustic effect. It is shown that this effect can be exploited for the design of systems with exotic acoustic scattering properties through two experimental demonstrations. The first example showcases a balanced asymmetric transmitter with transmission coefficients inverse of each other, yielding a nonreciprocity factor of 18 dB, without reflections. The second example shows a coherent perfect absorber, where maximum absorption is achieved for a wide range of temperature gradients by controlling the relative amplitudes and phasing of incoming waves.